To solve the equation 27/4 * (x + 7/5) = 9/8, you can follow these steps:

1. Distribute the 27/4 to the terms inside the parentheses:
(27/4) * x + (27/4) * (7/5) = 9/8

2. Simplify the expression:
(27/4) * x + (189/20) = 9/8

3. To get rid of the fraction in front of x, multiply both sides of the equation by the reciprocal of 27/4, which is 4/27:
(4/27) * [(27/4) * x + (189/20)] = (4/27) * (9/8)

Simplifying the right side:
(4/27) * [(27/4) * x + (189/20)] = 3/6

Simplifying the left side:
(4/27) * (27/4) * x + (4/27) * (189/20) = 3/6

The (27/4) and (4/27) cancel each other out, leaving:
x + (4/27) * (189/20) = 3/6

4. Simplify the expression:
x + (4/27) * (189/20) = 1/2

Multiply the fractions:
x + (4 * 189) / (27 * 20) = 1/2

Simplify the numerator:
x + 756 / (27 * 20) = 1/2

Multiply the denominators:
x + 756 / 540 = 1/2

5. To get rid of the fraction on the left side, multiply both sides of the equation by 540:
540 * (x + 756 / 540) = 540 * (1/2)

Simplify the right side:
540 * (x + 756 / 540) = 270

Distribute the 540 to the terms inside the parentheses:
540x + 756 = 270

6. Subtract 756 from both sides of the equation:
540x + 756 - 756 = 270 - 756

Simplify:
540x = -486

7. Divide both sides of the equation by 540:
(540x) / 540 = -486 / 540

Simplify:
x = -9/10

Therefore, the solution to the equation 27/4 * (x + 7/5) = 9/8 is x = -9/10.